Antioptimization of earthquake excitation and response.
Elastic wave equation
The goal of this talk is to describe the Lamé operator which drives the propagation of linear elastic waves. The main motivation for me is the work I have done in collaboration with Michel Campillo’s group from LGIT (Grenoble) on passive imaging in seismology. From this work, several mathematical problems emerged: equipartition of energy between and waves, high frequency description of surface waves in a stratified medium and related inverse spectral problems.We discuss the following topics:What...
Estimación no paramétrica de la función de riesgo: aplicaciones a sismología.
Se estudia la estimación de tipo no paramétrico de la función de riesgo o razón de fallo de una variable aleatoria real. A partir de una muestra X1, X2, ..., Xn de datos no censurados y no necesariamente independientes, se considera un estimador cociente entre el estimador núcleo de la función de densidad y un estimador núcleo de la función de supervivencia, sobre el que se estudia el problema de selección del parámetro ventana. Por medio de un estudio de simulación se observa la ventaja de utilizar...
Estimation semi-paramétrique d'un modèle autorégressif stationnaire multiindice non nécessairement causal
Higher-order splitting method for elastic wave propagation.
Justification of a construction of the solution of the problem on a point source of waves in a layered medium with vertical boundary.
Mathematical problems in geophysical wave propagation.
Mathematical simulation of ground vibrations taking into account nonlinear properties under intensive influences.
Microlocal analysis and seismic imaging
We study certain Fourier integral operators arising in the inversion of data from reflection seismology.
On the propagation of seismic waves in block fluid media.
Parallelization of a ray tracer using the SANEG algorithm.
Propagation of seismic waves in block elastic-fluid media. III.
Rayleigh wave scattering at the foot of a mountain.
Reflection and transmission of seismic waves under initial stress at the earth's core-mantle boundary.
Spectral analysis of strongly propagative systems.
The direct dynamical problem of seismics for horizontally stratified media.
The weak boundary effect in a field as a source approaches the boundary.
Theoretical aspects of a multiscale analysis of the eigenoscillations of the Earth.
The elastic behaviour of the Earth, including its eigenoscillations, is usually described by the Cauchy-Navier equation. Using a standard approach in seismology we apply the Helmholtz decomposition theorem to transform the Fourier transformed Cauchy-Navier equation into two non-coupled Helmholtz equations and then derive sequences of fundamental solutions for this pair of equations using the Mie representation. Those solutions are denoted by the Hansen vectors Ln,j, Mn,j, and Nn,j in geophysics....
Time series modelling of the Kobe-Osaka earthquake recordings.
Time-frequency representations of earthquake motion records.